Temperature-Entropy (T-S) Diagrams and the Critical Point Commonly, the steam process in a boiler is represented on a temperature-entropy (T-S) diagram. An example of such a T-S diagram can be seen below: This type of diagram can be read just like a phase diagram. On the far left, water is in the liquid phase. At temperatures below the critical point, increasing entropy causes water to enter a region with both liquid and vapor. The lever rule can be applied in this region to determine the amounts of liquid and solid. On the far left of the diagram is the vapor phase.
Above a certain temperature, called the critical temperature, there is no longer a phase boundary between the liquid and vapor phases. Instead, one blends seamlessly into the other.
It is important to note that the dotted lines on the diagram represent uniform pressures. A process where the pressure remains constant, such as boiling water on the stove, would follow the dotted line that corresponded to atmospheric pressure. This line would follow the left side of the bell curve and then the horizontal isobaric line through the liquid-vapor phase. During this transition, any heat that is added to the system will increase the entropy but will not increase the pressure. This is why water cannot reach a temperature higher than 100C at atmospheric pressure. After all the liquid water has turned to steam, the temperature will once again begin to increase.
In order to reach the critical point in an isobaric process, the liquid water must start out at a pressure of at least 22 MPa. This will allow it to follow a pressure line just outside the bell curve and reach the critical point.
The Rankine Cycle A Rankine cycle refers to the process that steam goes through to provide useful energy. It is the same process for steam locomotives and coal-fired power plants. A simplified diagram of the process can be seen below:
It’s important to note that the heating (boiler) and cooling (condenser) portions of the cycle are isobaric. Only at the pump and the turbine are the pressures increased or decreased.
An example of the process in a coal power plant can be seen below:
The path from 1 to 2 to 3 refers to the steam entering and being heated by the boiler. At 3, the steam enters the turbine and cools off and decreased in pressure to 4. At 4, the steam exits the turbine and enters the condenser, where it returns to a liquid phase. Between 5 and 1, the liquid is pumped back into the boiler and increases it’s pressure.
The energy produced by this process is the area of the red region contained by the process paths (W). In the diagram, Qr refers to the unused (lost) energy. This is dependent on the surrounding (atmospheric) temperature, and cannot be altered unless the environment changes. The efficiency of the system is the useful energy (W) divided by the total energy put into the system (Qa, or W+Qr). It is clear that the efficiency of the system can be increased by increasing the temperature to which the steam is heated.
Steam Oxidization
Supercritical Rankine Cycle: A synopsis of the cycle, it’s background, potential applications and engineering challenges. Shane Hough. 7 April 2009.
Solid overall summary of supercritical thermodynamics. Compared supercritical efficiencies to subcritical efficiencies. Does not discuss ultra-supercritical plants.
High efficiency electric power generation: The environmental role. Ja´nos M. Bee´r. Massachusetts Institute of Technology, Cambridge, MA. 17 October 2006
In-depth examination of power generation. Broad focus, but also discusses ultra-supercritical power efficiencies. A lot of specific details and experimental data.
"A Thermodynamic Approach to Steam-Power System Design." Ind. Eng. Chem. Process Des. Dev. Masatoshi Nishio, Johtaro Itoh, Katsuo Shiroko, and Tomlo Umeda. Process Systems Engineering Department, Chiyoda Chemical Engineering & Construction Co., Ltd. Tsurumi, Yokohama, Japan. 1980.
Thermodynamically-heavy discussion of steam power. Uses fairly broad thermodynamic principles. Not specific to supercritical steam or power plants. Useful, but also not particularly up-to-date.
Commonly, the steam process in a boiler is represented on a temperature-entropy (T-S) diagram. An example of such a T-S diagram can be seen below:
This type of diagram can be read just like a phase diagram. On the far left, water is in the liquid phase. At temperatures below the critical point, increasing entropy causes water to enter a region with both liquid and vapor. The lever rule can be applied in this region to determine the amounts of liquid and solid. On the far left of the diagram is the vapor phase.
Above a certain temperature, called the critical temperature, there is no longer a phase boundary between the liquid and vapor phases. Instead, one blends seamlessly into the other.
It is important to note that the dotted lines on the diagram represent uniform pressures. A process where the pressure remains constant, such as boiling water on the stove, would follow the dotted line that corresponded to atmospheric pressure. This line would follow the left side of the bell curve and then the horizontal isobaric line through the liquid-vapor phase. During this transition, any heat that is added to the system will increase the entropy but will not increase the pressure. This is why water cannot reach a temperature higher than 100C at atmospheric pressure. After all the liquid water has turned to steam, the temperature will once again begin to increase.
In order to reach the critical point in an isobaric process, the liquid water must start out at a pressure of at least 22 MPa. This will allow it to follow a pressure line just outside the bell curve and reach the critical point.
The Rankine Cycle
A Rankine cycle refers to the process that steam goes through to provide useful energy. It is the same process for steam locomotives and coal-fired power plants. A simplified diagram of the process can be seen below:
It’s important to note that the heating (boiler) and cooling (condenser) portions of the cycle are isobaric. Only at the pump and the turbine are the pressures increased or decreased.
An example of the process in a coal power plant can be seen below:
The path from 1 to 2 to 3 refers to the steam entering and being heated by the boiler. At 3, the steam enters the turbine and cools off and decreased in pressure to 4. At 4, the steam exits the turbine and enters the condenser, where it returns to a liquid phase. Between 5 and 1, the liquid is pumped back into the boiler and increases it’s pressure.
The energy produced by this process is the area of the red region contained by the process paths (W). In the diagram, Qr refers to the unused (lost) energy. This is dependent on the surrounding (atmospheric) temperature, and cannot be altered unless the environment changes. The efficiency of the system is the useful energy (W) divided by the total energy put into the system (Qa, or W+Qr). It is clear that the efficiency of the system can be increased by increasing the temperature to which the steam is heated.
Steam Oxidization
Supercritical Rankine Cycle: A synopsis of the cycle, it’s background, potential applications and engineering challenges. Shane Hough. 7 April 2009.
Solid overall summary of supercritical thermodynamics. Compared supercritical efficiencies to subcritical efficiencies. Does not discuss ultra-supercritical plants.
Supercritical Rankine Cycle.pdf
High efficiency electric power generation: The environmental role. Ja´nos M. Bee´r. Massachusetts Institute of Technology, Cambridge, MA. 17 October 2006
In-depth examination of power generation. Broad focus, but also discusses ultra-supercritical power efficiencies. A lot of specific details and experimental data.
High efficiency electric power generation.pdf
"A Thermodynamic Approach to Steam-Power System Design." Ind. Eng. Chem. Process Des. Dev. Masatoshi Nishio, Johtaro Itoh, Katsuo Shiroko, and Tomlo Umeda. Process Systems Engineering Department, Chiyoda Chemical Engineering & Construction Co., Ltd. Tsurumi, Yokohama, Japan. 1980.
Thermodynamically-heavy discussion of steam power. Uses fairly broad thermodynamic principles. Not specific to supercritical steam or power plants. Useful, but also not particularly up-to-date.
A Thermodynamic Approach to Steam-Power System Design.pdf
Ultra-Supercritical Steam Corrosion.pdf
Ultra-Supercritical Steam Oxidization.pdf